MATATAG Grade 7 : NUmber system conversion process.pptx

TLE Grade 7

1. Open the link to view videos before answering the activity sheet https://tinyurl.com/ICTG7wk3

2. 78- ____________ 100112 - ____________ F - _______ 328 - __________ 1110102 - ___________ Decimal Binary Hexadecimal Decimal Binary Activity 1: On the given below, identify the type of number system by writing your answer on the given space in each item. Week 3 Day 11

3. Activity 2: Word Completion – Converting Decimal to Binary Directions: Supply the missing word to complete the Steps in Conversion of Decimal to Binary. 1. Divide the number by ____________________________________________. 2. Write the quotient and the __________________on its corresponding ___________________. 3. Get the quotient and divide it again by _______________________________. Write the quotient and remainder in its column. 4. Continue dividing until the quotient results to _________________________. Always write its quotient and remainder in their column. 5. Copy the remainder from the bottom to _____________________________. That would be the binary equivalent of the decimal number 2 remainder value 2 top

4. Activity 3: Convert the given below (Decimal) into Binary. Show the process of your conversion. 1) 11 Step 1: Divide 11 by 2. 11 10 = ______________ 2 11 5 1 2 2 1 2 1 2 1 Quotient: 5, Remainder: 1 Step 2: Divide 5 by 2. Quotient: 2, Remainder: 1 Step 3: Divide 2 by 2. Quotient: 1, Remainder: 0 Step 4: Divide 1 by 2. Quotient: 0, Remainder: 1 Reverse the remainders: 1011 Therefore, 11 in binary is 1011

5. Activity 3: Convert the given below (Decimal) into Binary. Show the process of your conversion. 2) 27 Step 1: Divide 27 by 2. 27 10 = ______________ 2 27 13 1 2 6 1 2 3 2 1 1 Quotient: 13, Remainder: 1 Step 2: Divide 13 by 2. Quotient: 6, Remainder: 1 Step 3: Divide 6 by 2. Quotient: 3, Remainder: 0 Step 4: Divide 3 by 2. Quotient: 1, Remainder: 1 Reverse the remainders: 11011 Therefore, 27 in binary is 11011 Step 4: Divide 1 by 2. Quotient: 0, Remainder: 1 2 1

6. Method The positional notation method is one in which the value of a digit in a number is determined by a weight based on its position. The steps to convert binary to decimal are as follows: Step 1:   Multiply  each digit starting from the rightmost digit by the powers of 2. Here, we start with 2  and increase the exponent by 1 as we move onto the left side. Step 2:  The  sum   of all these values obtained for each digit gives the equivalent value of the given binary number in the decimal system.

7. Example:  Convert the binary number 101101 2  to a decimal number. Solution:  Observe the following steps to understand the binary to decimal conversion. In any binary number, the rightmost digit is called the 'Least Significant Bit' (LSB) and the left-most digit is called the 'Most Significant Bit' (MSB). For a binary number with 'n' digits, the least significant bit has a weight of 2  and the most significant bit has a weight of 2 n-1 . Activity 4: Convert the given below (Decimal) into Binary. Show the process of your conversion.

8. Step 1:  List out the   exponents   of 2 for all the digits starting from the rightmost position. The first power would be 2  and as we move on to the left side it will be 2 1 , 2 2 , 2 3 , 2 4 , 2 5 ,... In the given example, there are 6 digits, therefore, starting from the rightmost digit, the weight of each position from right to left is 2 , 2 1 , 2 2 , 2 3 , 2 4 , and 2 5 .

9. Step 2:  Now multiply each digit in the binary number starting from the right with its respective weight based on its position and evaluate the  product . Observe the figure shown below to relate to the step.

10. Step 3:  Finally, sum up all the products obtained for all the digits in the binary number, which gives the decimal equivalent of the given bu = inary number. i.e., 101101 2  = 45 10

11. Activity 4: Convert the given below (Decimal) into Binary. Show the process of your conversion. 1) 101 2 1 1 2 2 1 2 2 1 x 2 = 2 1 x 2 2 = 4 6 10

12. Activity 4: Convert the given below (Decimal) into Binary. Show the process of your conversion. 2) 1100 2 1 1 1 2 2 1 2 3 1 x 2 = 2 1 x 2 3 = 8 14 10 2 2 1 x 2 2 = 4

13. Week 3 Day 12 and 13 Fill in the blank with the correct words.   To convert a decimal number to octal, we first need to __________________ the decimal number by 8. The __________________ of the division is the first digit of the octal number. The ___________________________ of the division is used for the next step. This process of dividing by 8 and using the remainder continues until the __________________________ becomes 0. The octal number is formed by writing the remainder in ___________ order. divide remainder divisor quotient reverse

14. B. Decimal and Octal Converting Decimal numbers to Octal and Octal to Decimal Numbers. Choose the correct letter of the answer and write on the space provided before each number.  1) What is the decimal equivalent of the octal number 64? A. 4 B. 14 C. 52 D. 100 2) If an octal number is 127, what is its value in decimal? A. 16 B. 55 C. 87 D. 102 3) Convert the octal number 345 to decimal. A. 125 B. 197 C. 209 D. 225 4) What is the decimal value of the octal number 777? A. 9 B. 383 C. 504 D. 511 5) If an octal number is 476, what is its decimal equivalent? A. 312 B. 302 C. 256 D. 318 No answer on the given activity

15. 1. Write down the octal _________________________.  2. Find the _________________________ of every digit. We should count the position from the right direction of the number. And the position count starts from 0.  3. ____________________________ every digit with 8 to the power of their corresponding position.  4. Finally, calculate the ______________________ of all the multiples. Position numbers multiply sum C) Converting Octal to decimal: Fill in the blank with the correct words. numbers position sum multiply

16. D. Converting Decimal to Octal and Octal to Decimal 653 10 B. 627 8

17. D. Converting Decimal to Octal and Octal to Decimal 653 10 B. 627 8 653/8 = 81.625 > 5 81/8 =10.125 > 1 10/8 =1.25 >2 1/8 =0 >1 L east S ignificant B it MSB LSB M ost S ignificant B it = 1215 8 6 2 8 6 x 8 2 + 2 x 8 1 + 8 x 8 6 x 64 + 2 x 8 + 8 384 + 16 + 8 408 8

18. Week 3 Day 14 remainder number zero values hexadecimal A. Fill in the blank with the correct words. Choose your answer from the word inside the box. Decimal to Hexadecimal Conversion with Steps Go through the steps given below to learn how to convert the numbers from decimal to hex. Step 1: First, divide the decimal ___________________ by 16, considering the number as an integer. Step 2: Keep aside the _____________________________. Step 3: Again divide the quotient by 16 and repeat till you get the quotient value equal to _______________. Step 4: Now take the _______________________ of the remainder’s left in the reverse order to get the ______________________ numbers. number remainder zero values

19. B. Converting hexadecimal to decimal: Fill in the blank with the correct words. Choose your answer from the word inside the box. power Multiply digit right products Step 1: Write down the _________________ of 16 from __________________ to left starting with 16 Step 2: _________ these 16 n with their corresponding hexadecimal ________. Step 3: Add all the __________________________ obtained in Step ii) to get the desired decimal number. right products Multiply digit power

20. Convert the following from decimal to hexadecimal or hexadecimal to decimal 960 10 2) 1AB 960 Divisor Decimal Quotient Remainder Equivalent to Hexadecimal 16 960 60 16 60 3.75 12 C 16 3 0.1875 3 3 =3C0 16

21. Convert the following from decimal to hexadecimal or hexadecimal to decimal 960 10 2) 1AB =3C0 16 1 A B 16 2 16 1 16 1 X 16 2 + 10 x 16 1 + 11 x 16 1 X 256 + 10 x 16 + 11 x 1 256 + 160 + 11 =427 10 427 10

22. Work in groups and present your answer with solutions Class will be divided into three

23. No. Decimal Binary Octal Hexadecimal 1 200 10 2 11111010 2 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

24. Decimal to Binary 200 10 =11001000 2 200/2 =100 : 0 100/2 =50 : 0 50/2 =25 : 0 25/2 =12 : 1 12/2 =6 : 0 6/2 =3 : 0 3/2 =1 : 1 1/2 =0 : 1 1 1 0 0 1 0 0 0 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 To check 1 x 2 7 + 1 x 2 6 + 0 x 2 5 + 0 x 2 4 + 1 x 2 3 + 0 x 2 2 + 0 x 2 1 + 0 x 2 1 x 128 + 1 x 64 + 0 x 32 + 0 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 0 x 1 128 + 64 + 0 + + 8 + + + 200 10

25. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 2 11111010 2 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

26. Decimal to Octal 200 10 =310 8 200/8 =25 : 0 25/8 =3.123 : 1 3/8 =.375 : 3 3 1 0 8 2 8 1 8 To check 3 x 8 2 + 1 x 8 1 + 0 x 8 3 x 64 + 1 x 8 + 0 x 1 192 + 8 + 0 200 10

27. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 2 11111010 2 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

28. Decimal to Hexadecimal 200 10 =C8 16 200/16 =12.5 : 8 12/16 =.75 : 12 = C C 8 16 1 16 To check 12 x 16 1 + 8 x 16 12 x 16 + 8 x 1 192 + 8 200 10

29. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 11111010 2 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

30. Binary to Decimal 250 10 =11111010 2 250/2 =125 : 0 125/2 =62 : 1 62/2 =31 : 0 31/2 =15 : 1 15/2 =7 : 1 7/2 =3 : 1 3/2 =1 : 1 1/2 =0 : 1 1 1 1 1 1 0 1 0 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 To check 1 x 2 7 + 1 x 2 6 + 1 x 2 5 + 1 x 2 4 + 1 x 2 3 + 0 x 2 2 + 1 x 2 1 + 0 x 2 1 x 128 + 1 x 64 + 1 x 32 + 1 x 16 + 1 x 8 + 0 x 4 +1 x 2 + 0 x 1 128 + 64 + 32 + 16 + 8 + + 2 + 250 10

31. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

32. Decimal to Octal

33. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

34. Decimal to Hexadecimal

35. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

36. Octal to Decimal

37. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

38. Decimal to Binary

39. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

40. Decimal to Hexadecimal

41. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 190 16 5 1F4 16 6 1130 8 7 1010111100 2

42. Hexadecimal to Decimal

43. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 190 16 5 1F4 16 6 1130 8 7 1010111100 2

44. Decimal to Binary

45. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 190 16 5 1F4 16 6 1130 8 7 1010111100 2

46. Decimal to Octal

47. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 1F4 16 6 1130 8 7 1010111100 2

48. Hexadecimal to Decimal

49. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 1F4 16 6 1130 8 7 1010111100 2

50. Decimal to Binary

51. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 1F4 16 6 1130 8 7 1010111100 2

52. Decimal to Octal

53. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 1130 8 7 1010111100 2

54. Octal to Decimal

55. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1130 8 7 1010111100 2

56. Decimal to Binary

57. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1001011000 2 1130 8 7 1010111100 2

58. Decimal to Hexadecimal

59. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1001011000 2 1130 8 258 16 7 1010111100 2

60. Binary to Decimal 700 10 = 1010111100 2 700/2 =350 : 0 350/2 =175 : 0 175/2 =87 : 1 87/2 =43 : 1 43/2 =21 : 1 21/2 =10 : 1 10/2 =5 : 0 5/2 =2 : 1 1 0 1 0 1 1 1 1 0 0 2 9 2 8 2 7 2 6 2 5 2 4 2 3 2 2 2 1 2 To check 1 x 2 9 + 0 x 2 8 + 1 x 2 7 + 0 x 2 6 + 1 x 2 5 + 1 x 2 4 + 1 x 2 3 + 1 x 2 2 + 0 x 2 1 + 0 x 2 1 x 512 + 0 x 256 + 1 x 128 + 0 x 64 + 1 x 32 + 1 x 16 +1 x 8 + 1 x 4 + x 2 + 0 x 1 512 + 0 + 128 + 0 + 32 + 16 + 8 + 4 + + 700 10 2/2 =1 : 0 1/2 =0 : 1

61. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1001011000 2 1130 8 258 16 7 700 10 1010111100 2

62. Decimal to Octal

63. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1001011000 2 1130 8 258 16 7 700 10 1010111100 2 1274 8

64. Decimal to Hexadecimal

65. No. Decimal Binary Octal Hexadecimal 1 200 10 11001000 2 310 8 C8 16 2 250 10 11111010 2 372 8 FA 16 3 300 10 100101100 2 454 8 12C 16 4 400 10 110010000 2 620 8 190 16 5 500 10 111110100 2 764 8 1F4 16 6 600 10 1001011000 2 1130 8 258 16 7 700 10 1010111100 2 1274 8 2BC 16